"....so are we right in assuming we need a wireless router that connects to the PC by ethernet cable and just keep the pc connected to the internet as normal?"
Totally wrong. The ADSL modem will have to go because routers can't take them - only ethernet modems for cable services. You need a modem/router, such as a Belkin 7632.
"....and the PC use a wireless PCI card?"
Not really. Once you have configured the modem/router, you can use this method if you have reason for not having the router positioned near to a desktop PC. During the config process, it needs to be wired to the desktop through an ethernet LAN cable into the desktop's LAN port. Don't have a LAN port? You'll need a LAN PCI card.
Laptops are a piece of cake, because they're virtually all wifi enabled.
Once you've got the modem/router, come back here and ask us about the absolutely essential process of securing your network. An unsecured network is a totally open PC. If you happen to choose Belkin, I'll talk you through it, but there are other forum members who will help with D-link or Linksys. I would ont recommend that you choose Netgear, because if you happen to run into trouble with a bad one, we'll be here all week!